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• W3134787383 endingPage "107202" @default.
• W3134787383 startingPage "107202" @default.
• W3134787383 abstract "A general and efficient nonparametric density estimation procedure for local bases, including B-splines, is proposed, which employs a novel statistical Galerkin method combined with basis duality theory. To select the bandwidth, an efficient cross-validation procedure is introduced, based on closed-form expressions in terms of the primal and dual B-spline basis. By utilizing a closed-form expression for the dual basis, the least-squares cross validation formula is calculated in closed-form, enabling an efficient estimation of the optimal bandwidth. The full computational procedure achieves optimal complexity, and is very accurate in comparison with existing estimation procedures, including state-of-the-art kernel density estimators. The presented theoretical results are supported by extensive numerical experiments, which demonstrate the efficiency and accuracy of the new methodology. This new approach provides a complete and optimally efficient framework for density estimation with a B-spline basis, based on simple and elegant closed-form estimators with theoretical convergence results that are substantiated in numerical experiments." @default.
• W3134787383 created "2021-03-15" @default.
• W3134787383 creator A5014870015 @default.
• W3134787383 creator A5047745167 @default.
• W3134787383 creator A5051493924 @default.
• W3134787383 date "2021-07-01" @default.
• W3134787383 modified "2023-09-25" @default.
• W3134787383 title "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method" @default.
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• W3134787383 doi "https://doi.org/10.1016/j.csda.2021.107202" @default.
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